A direct approach to quaternionic manifolds

The recent definition of slice regular function of several quaternionic variables suggests a new notion of quaternionic manifold. We give the definition of quaternionic regular manifold, as a space locally modeled on $\mathbb{H}^n$, in a slice regular sense. We exhibit some significant classes of examples, including manifolds which carry a quaternionic affine structure.Comment: 13 page

An Introduction to Gerbes on Orbifolds

This paper is a gentle introduction to some recent results involving the theory of gerbes over orbifolds for topologists, geometers and physicists. We introduce gerbes on manifolds, orbifolds, the Dixmier-Douady class, Beilinson-Deligne orbifold cohomology, Cheeger-Simons orbifold cohomology and string connections.Comment: To appear in the Annales Mathematiques Blaise Pasca

On globally non-trivial almost-commutative manifolds

Within the framework of Connes' noncommutative geometry, we define and study globally non-trivial (or topologically non-trivial) almost-commutative manifolds. In particular, we focus on those almost-commutative manifolds that lead to a description of a (classical) gauge theory on the underlying base manifold. Such an almost-commutative manifold is described in terms of a 'principal module', which we build from a principal fibre bundle and a finite spectral triple. We also define the purely algebraic notion of 'gauge modules', and show that this yields a proper subclass of the principal modules. We describe how a principal module leads to the description of a gauge theory, and we provide two basic yet illustrative examples.Comment: 34 pages, minor revision

Realtime projective multi-texturing of pointclouds and meshes for a realistic street-view web navigation

International audienceStreet-view web applications have now gained widespread popularity. Targeting the general public, they offer ease of use, but while they allow efficient navigation from a pedestrian level, the immersive quality of such renderings is still low. The user is usually stuck at specific positions and transitions bring out artefacts, in particular parallax and aliasing. We propose a method to enhance the realism of street view navigation systems using a hybrid rendering based on realtime projective texturing on meshes and pointclouds with occlusion handling, requiring extremely minimized pre-processing steps allowing fast data update, progressive streaming (mesh-based approximation, with point cloud details) and unaltered raw data precise visualization